An elementary approach to uniform in time propagation of chaos

Alain Durmus (1) , Andreas Eberle (2) , Arnaud Guillin (3) , Raphael Zimmer (2)

1 CB - CB - Centre Borelli - UMR 9010
2 Instutute for Applied Mathematics [Bonn]
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of reflection and synchronous couplings applied to the individual particles. It provides explicit quantitative bounds that significantly extend previous results for the convex case.

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Alain Durmus, Andreas Eberle, Arnaud Guillin, Raphael Zimmer. An elementary approach to uniform in time propagation of chaos. Proceedings of the American Mathematical Society, 2020, 148 (12), pp.5387-5398. ⟨10.1090/proc/14612⟩. ⟨hal-01801275⟩